real data simulation analysis

File Introduction

This is the R file including all the content related to the simulated data based on real data analysis. Please notice that this is a simulation, so the execution time would be around 4 hours. The main content of this file includes:

0. Installing required packages
1. Functions for Data simulation and Analysis (figure 9)
2. Clustering Number Selection Validation (table 4)
3. Clustering Validation Study (table 5)

Please notice that since this is the simulation based on real data, we would use the cleaned data and clustering result of the real data analysis, and you would found that we have saved those results in the following files and read in this code:

1. mindiff_day1_nona.csv
2. mindiff_state1_nona.csv
3. real_analysis_result.csv

PLEASE USING WINDOWS SYSTEM to execute the code so as to reproduce the figures and tables in the paper! Ubuntu and OS system have different setting on seed setting, so the execution result would be slightly different on these two system. Moreover, our key algorithm FunFEM would diverge or fail on some seed, so we strongly suggest to use WINDOWS system to execute the code.

In addition, FunFEM would try multiple variance and covariance matrix form to get the best result. In some forms, the result would be diverge and you may see some warning or message like

"Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*% : infinite or missing values in ‘x’" “Error in svd(X) : infinite or missing values in ‘x’”

This is not a real error and the code would keep running.

Coding Part for Real Data Analysis

0. Installing required packages

# ipak, a function for checking the the installation of the packages
ipak <- function(pkg){
  new.pkg <- pkg[!(pkg %in% installed.packages()[, "Package"])]
  if (length(new.pkg)) 
    install.packages(new.pkg, dependencies = TRUE)
  sapply(pkg, require, character.only = TRUE)
}

# add new packages here
packages <- c("ggplot2", "dplyr", "tidyverse", "tidyr", "ggridges",
              "scales","geofacet","lubridate","fda","fda.usc","RColorBrewer",
              "ggrepel","DT","ggthemes","fpc","clue",
              "gridExtra","factoextra", "NbClust","funFEM","mapproj")
ipak(packages)

##      ggplot2        dplyr    tidyverse        tidyr     ggridges       scales 
##         TRUE         TRUE         TRUE         TRUE         TRUE         TRUE 
##     geofacet    lubridate          fda      fda.usc RColorBrewer      ggrepel 
##         TRUE         TRUE         TRUE         TRUE         TRUE         TRUE 
##           DT     ggthemes          fpc         clue    gridExtra   factoextra 
##         TRUE         TRUE         TRUE         TRUE         TRUE         TRUE 
##      NbClust       funFEM      mapproj 
##         TRUE         TRUE         TRUE

1. Simulation based on real Data pattern

Functions for Simulation Study (Fig 9)

• The simulation curves sample at Fig 9 is at the end of this chunk of code.

##Loading the unsmoothed non-missing data and cluster information
mindiff.date.1 = read.csv("mindiff_day1_nona.csv")
mindiff.date.1$date = as.Date(mindiff.date.1$x,format = "%Y-%m-%d")
mindiff.state.1 = read.csv("mindiff_state1_nona.csv")
cluster.result = read.csv("real_analysis_result.csv")

## Generate curves based on real data
generate.curve.real<-function(n.group, seed, plotting = F){
  ## Simulating 4 clusters based on real application result
  # IN cluster 1
  clu.1 = cluster.result[cluster.result$fem.4 == 1,]$state
  clu.1.raw = mindiff.state.1[,names(mindiff.state.1)%in%clu.1]
  clu.1.rawmat.1 = matrix(unlist(clu.1.raw),ncol = ncol(clu.1.raw))
  bks.1 = as.Date(quantile(unclass(as.Date(mindiff.date.1$date)), seq(0,1,length = 15)), origin = "1970-01-01")
  err1.basis = create.bspline.basis(rangeval = c(min(mindiff.date.1$date),max(mindiff.date.1$date)), breaks = bks.1, norder = 4) 
  clu.1.fd<-smooth.basis(argvals = mindiff.date.1$date, y = clu.1.rawmat.1, err1.basis)$fd
  clu.1.fpca = pca.fd(clu.1.fd,nharm=3) 
  clu.1.fpca.loading = clu.1.fpca$harmonics$coefs
  clu.1.fpca.lambda = clu.1.fpca$values[1:3]
  clu.1.mean.coef = clu.1.fpca$meanfd$coefs
  
  ## Simulate n curves:
  set.seed(seed)
  clu.1.score1 = rnorm(n.group,0,sqrt(clu.1.fpca.lambda[1]))
  clu.1.score2 = rnorm(n.group,0,sqrt(clu.1.fpca.lambda[2]))
  clu.1.score3 = rnorm(n.group,0,sqrt(clu.1.fpca.lambda[3]))
  clu.1.scores = rbind(clu.1.score1,clu.1.score2,clu.1.score3)
  clu.1.simcoeff = t(clu.1.scores)%*%t(clu.1.fpca.loading)+matrix(clu.1.mean.coef,nrow=n.group,ncol=length(clu.1.mean.coef),byrow=TRUE)
  clu.1.sim.df = clu.1.fd
  clu.1.sim.df$coefs = t(clu.1.simcoeff)
  clu.1.sim.data = predict(clu.1.sim.df,mindiff.date.1$date)
 
  name.clu1 = paste0("clu1.",1:n.group)
  colnames(clu.1.sim.data) <- name.clu1
  clu.1.sim.data = data.frame(clu.1.sim.data)
  
  # IN cluster 2
  clu.2 = cluster.result[cluster.result$fem.4 == 2,]$state
  clu.2.raw = mindiff.state.1[,names(mindiff.state.1)%in%clu.2]
  clu.2.rawmat.1 = matrix(unlist(clu.2.raw),ncol = ncol(clu.2.raw))
  clu.2.fd<-smooth.basis(argvals = mindiff.date.1$date, y = clu.2.rawmat.1, err1.basis)$fd
  clu.2.fpca = pca.fd(clu.2.fd,nharm=3) 
  clu.2.fpca.loading = clu.2.fpca$harmonics$coefs
  clu.2.fpca.lambda = clu.2.fpca$values[1:3]
  clu.2.mean.coef = clu.2.fpca$meanfd$coefs
  
  ## Simulate n curves:
  set.seed(seed)
  clu.2.score1 = rnorm(n.group,0,sqrt(clu.2.fpca.lambda[1]))
  clu.2.score2 = rnorm(n.group,0,sqrt(clu.2.fpca.lambda[2]))
  clu.2.score3 = rnorm(n.group,0,sqrt(clu.2.fpca.lambda[3]))
  clu.2.scores = rbind(clu.2.score1,clu.2.score2,clu.2.score3)
  clu.2.simcoeff = t(clu.2.scores)%*%t(clu.2.fpca.loading)+matrix(clu.2.mean.coef,nrow=n.group,ncol=length(clu.2.mean.coef),byrow=TRUE)
  clu.2.sim.df = clu.2.fd
  clu.2.sim.df$coefs = t(clu.2.simcoeff)
  clu.2.sim.data = predict(clu.2.sim.df,mindiff.date.1$date)
  
  name.clu2 = paste0("clu2.",1:n.group)
  colnames(clu.2.sim.data) <- name.clu2
  clu.2.sim.data = data.frame(clu.2.sim.data)
  
  # IN cluster 3
  clu.3 = cluster.result[cluster.result$fem.4 == 3,]$state
  clu.3.raw = mindiff.state.1[,names(mindiff.state.1)%in%clu.3]
  clu.3.rawmat.1 = matrix(unlist(clu.3.raw),ncol = ncol(clu.3.raw))
  clu.3.fd<-smooth.basis(argvals = mindiff.date.1$date, y = clu.3.rawmat.1, err1.basis)$fd
  clu.3.fpca = pca.fd(clu.3.fd,nharm=3) 
  clu.3.fpca.loading = clu.3.fpca$harmonics$coefs
  clu.3.fpca.lambda = clu.3.fpca$values[1:3]
  clu.3.mean.coef = clu.3.fpca$meanfd$coefs
  
  ## Simulate n curves:
  set.seed(seed)
  clu.3.score1 = rnorm(n.group,0,sqrt(clu.3.fpca.lambda[1]))
  clu.3.score2 = rnorm(n.group,0,sqrt(clu.3.fpca.lambda[2]))
  clu.3.score3 = rnorm(n.group,0,sqrt(clu.3.fpca.lambda[3]))
  clu.3.scores = rbind(clu.3.score1,clu.3.score2,clu.3.score3)
  clu.3.simcoeff = t(clu.3.scores)%*%t(clu.3.fpca.loading)+matrix(clu.3.mean.coef,nrow=n.group,ncol=length(clu.3.mean.coef),byrow=TRUE)
  clu.3.sim.df = clu.3.fd
  clu.3.sim.df$coefs = t(clu.3.simcoeff)
  clu.3.sim.data = predict(clu.3.sim.df,mindiff.date.1$date)
  
  name.clu3 = paste0("clu3.",1:n.group)
  colnames(clu.3.sim.data) <- name.clu3
  clu.3.sim.data = data.frame(clu.3.sim.data)
  
  # IN cluster 4
  clu.4 = cluster.result[cluster.result$fem.4 == 4,]$state
  clu.4.raw = mindiff.state.1[,names(mindiff.state.1)%in%clu.4]
  clu.4.rawmat.1 = matrix(unlist(clu.4.raw),ncol = ncol(clu.4.raw))
  clu.4.fd<-smooth.basis(argvals = mindiff.date.1$date, y = clu.4.rawmat.1, err1.basis)$fd
  clu.4.fpca = pca.fd(clu.4.fd,nharm=3) 
  clu.4.fpca.loading = clu.4.fpca$harmonics$coefs
  clu.4.fpca.lambda = clu.4.fpca$values[1:3]
  clu.4.mean.coef = clu.4.fpca$meanfd$coefs
  
  ## Simulate n curves:
  set.seed(seed)
  clu.4.score1 = rnorm(n.group,0,sqrt(clu.4.fpca.lambda[1]))
  clu.4.score2 = rnorm(n.group,0,sqrt(clu.4.fpca.lambda[2]))
  clu.4.score3 = rnorm(n.group,0,sqrt(clu.4.fpca.lambda[3]))
  clu.4.scores = rbind(clu.4.score1,clu.4.score2,clu.4.score3)
  clu.4.simcoeff = t(clu.4.scores)%*%t(clu.4.fpca.loading)+matrix(clu.4.mean.coef,nrow=n.group,ncol=length(clu.4.mean.coef),byrow=TRUE)
  clu.4.sim.df = clu.4.fd
  clu.4.sim.df$coefs = t(clu.4.simcoeff)
  clu.4.sim.data = predict(clu.4.sim.df,mindiff.date.1$date)
  
  name.clu4 = paste0("clu4.",1:n.group)
  colnames(clu.4.sim.data) <- name.clu4
  clu.4.sim.data = data.frame(clu.4.sim.data)
  
  simu.all = cbind(clu.1.sim.data,clu.2.sim.data,clu.3.sim.data,clu.4.sim.data)
  simu.all$t = mindiff.date.1$date
  
  if(plotting == T){
    par(mfrow=c(2,2))
    plot(clu.1.sim.df,ylim = c(0,10))
    plot(clu.2.sim.df,ylim = c(0,10))
    plot(clu.3.sim.df,ylim = c(0,10))
    plot(clu.4.sim.df,ylim = c(0,10))
  }
  
  return (simu.all)
}

## Functions for Cluster Number Selection Study
cluster.select.num.real = function(simu.all,n.group,seed,plotting = FALSE){
  t = simu.all$t
  simu.all = simu.all[,-which(names(simu.all) %in% c("t"))]
  simu.all.mat = matrix(unlist(simu.all),ncol = 4*n.group)
  
  bks.1 = as.Date(quantile(unclass(as.Date(mindiff.date.1$date)), seq(0,1,length = 12)), origin = "1970-01-01")
  err1.basis = create.bspline.basis(rangeval = c(min(mindiff.date.1$date),max(mindiff.date.1$date)), breaks = bks.1, norder = 4) 
  simu.fd<-smooth.basis(argvals = t, y = simu.all.mat, err1.basis)$fd
  
  if(plotting == TRUE){plot(simu.fd)}
  
  ## FunFEM
  set.seed(seed)
  fem.clu.bic = funFEM(simu.fd,K = 2:6,model = "all",crit = "bic", init = "kmeans",eps = 1e-5)
  fem.num.bic = fem.clu.bic$K
  
  fem.clu.icl = funFEM(simu.fd,K = 2:6,model = "all",crit = "icl", init = "kmeans",eps = 1e-5)
  fem.num.icl = fem.clu.icl$K
  
  set.seed(seed)
  ## kmeans on smoothed FPC scores
  range = c(as.numeric(min(t)),as.numeric(max(t)))
  bspFpcPen = fdPar(fdobj=err1.basis, Lfdobj=2, lambda = 2*10^6)
  smooth.fpc = pca.fd(simu.fd,nharm=3,harmfdPar=bspFpcPen)
  fd.scores = smooth.fpc$scores
  # all index  
  set.seed(seed)
  fpc.kmeans.best <- NbClust(fd.scores, distance = "euclidean", 
                             min.nc=2, max.nc=6, 
                             method = "kmeans", 
                             index = "all")
  fpc.clu.select =  max(fpc.kmeans.best$Best.partition)
  
  # ## kmeans on coef -- would experience too many error, temporarly skip
  # fd.coefs = t(simu.fd$coefs)
  # # all index  
  # coeff.kmeans.best <- NbClust(fd.coefs, distance = "euclidean", 
  #                              min.nc=2, max.nc=6, 
  #                              method = "centroid", # due to the robust
  #                              index = "all")
  # bsp.clu.select =  max(coeff.kmeans.best$Best.partition)
  
  simu.clunum.compare = rbind(fem.num.bic,fem.num.icl,
                              fpc.clu.select)
  # bsp.clu.select: Easy to experience error, skip
  return(simu.clunum.compare)
}

# Simulation plot sample for Fig 9
set.seed(888)
generate.curve.real(20,seed = 888,plotting = TRUE)

Cluster Number Detection Simulation Study (Table 4)

• The Table 4 has been seperated in three part, and here has 2 of them: clunum.sim.20.summary and clunum.simunum.bspcoeff.20.summary
• The simulation result for Raw data at Table 4 is at the end of this code file

##Clustering Number Selection Validation Simulation 
simunum.real.20= data.frame(matrix(ncol = 4, nrow = 1))
colnames(simunum.real.20) <- c("method","index","clu.num","n.group")
seed = 888
for (i in 1:200){ 
  set.seed(seed)
  df = generate.curve.real(20,seed = seed)
  clunum.result = data.frame(matrix(ncol = 4, nrow = 3))
  colnames(clunum.result) <- c("method","index","clu.num","n.group")
  # clunum.result$method = c("fem","fem","bsp","fpc")
  clunum.result$method = c("fem","fem","fpc")
  # clunum.result$index = c("bic","icl","all","all")
  clunum.result$index = c("bic","icl","all")
  clunum.result$clu.num = cluster.select.num.real(simu.all=df, seed = seed,n.group=20)
  clunum.result$n.group = rep(20,each = 3)
  
  simunum.real.20 = rbind(simunum.real.20,clunum.result)
  seed = seed+10000*i
}

## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 5 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 8 proposed 2 as the best number of clusters 
## * 6 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 4 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  2 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 5 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 15 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 7 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 1 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 3 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 7 proposed 2 as the best number of clusters 
## * 7 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  2 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 6 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 3 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 12 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 5 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 7 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 11 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 7 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 5 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 3 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 7 proposed 2 as the best number of clusters 
## * 7 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  2 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 15 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 1 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 5 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 5 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 3 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 1 proposed 4 as the best number of clusters 
## * 5 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 5 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 11 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 2 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 7 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 4 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 3 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 5 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 6 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 5 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 7 proposed 2 as the best number of clusters 
## * 6 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 17 proposed 3 as the best number of clusters 
## * 1 proposed 4 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 5 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 6 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 3 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 7 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 7 proposed 2 as the best number of clusters 
## * 6 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 3 proposed 2 as the best number of clusters 
## * 7 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 6 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 15 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 5 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 8 proposed 2 as the best number of clusters 
## * 6 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 2 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 8 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 6 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 7 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 15 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 7 proposed 3 as the best number of clusters 
## * 12 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 4 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 2 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 6 proposed 3 as the best number of clusters 
## * 1 proposed 4 as the best number of clusters 
## * 6 proposed 5 as the best number of clusters 
## * 5 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 7 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 1 proposed 4 as the best number of clusters 
## * 9 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 2 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 6 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 3 proposed 2 as the best number of clusters 
## * 14 proposed 3 as the best number of clusters 
## * 2 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 3 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 6 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 3 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 2 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 6 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 4 proposed 5 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 6 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 6 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 16 proposed 3 as the best number of clusters 
## * 1 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 15 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 16 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 5 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 6 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 12 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 10 proposed 3 as the best number of clusters 
## * 7 proposed 4 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 7 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 4 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 1 proposed 2 as the best number of clusters 
## * 13 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 2 proposed 5 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 9 proposed 3 as the best number of clusters 
## * 8 proposed 4 as the best number of clusters 
## * 2 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 6 proposed 2 as the best number of clusters 
## * 6 proposed 3 as the best number of clusters 
## * 10 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 1 proposed 4 as the best number of clusters 
## * 7 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## ******************************************************************* 
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 8 proposed 2 as the best number of clusters 
## * 11 proposed 3 as the best number of clusters 
## * 4 proposed 4 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## *******************************************************************

simunum.real.20 = na.omit(simunum.real.20)
write.csv(simunum.real.20, file = "simunum_real_20.csv", row.names = FALSE)

### Table 4: FEM (BIC and ICL part) and Kmeans on FPC scores part
## Summary analysis of the cluster number detection.
clunum.sim.20 = read.csv("simunum_real_20.csv",header = TRUE)
clunum.sim.20.summary = clunum.sim.20%>%group_by(n.group, method,
                             index, clu.num)%>%summarize(count = n())
clunum.sim.20.summary

## Cluster Number Detection Simulation: Kmeans on B-spline Coefficients 
simunum.bspcoeff.20= data.frame(matrix(ncol = 4, nrow = 1))
colnames(simunum.bspcoeff.20) <- c("method","index","clu.num","n.group")
seed = 888
for (i in 1:200){
  set.seed(seed)
  df = generate.curve.real(20,seed = seed)
  t = df$t
  df = df[,-which(names(df) %in% c("t"))]
  df.mat = matrix(unlist(df),ncol = 4*20)
  
  bks.1 = as.Date(quantile(unclass(as.Date(mindiff.date.1$date)), seq(0,1,length = 12)), origin = "1970-01-01")
  err1.basis = create.bspline.basis(rangeval = c(min(mindiff.date.1$date),max(mindiff.date.1$date)), breaks = bks.1, norder = 4) 
  simu.fd<-smooth.basis(argvals = t, y = df.mat, err1.basis)$fd
  fd.coefs = t(simu.fd$coefs)
  clunum.result.bspcoeff = data.frame(matrix(ncol = 4, nrow = 1))
  colnames(clunum.result.bspcoeff) <- c("method","index","clu.num","n.group")
  clunum.result.bspcoeff$method = "kmeans on B-spline Coeff"
  clunum.result.bspcoeff$index = "average silhouette width"
  set.seed(seed)
  pamk.best <- pamk(fd.coefs,krange=2:6)
  clunum.result.bspcoeff$clu.num = pamk.best$nc
  clunum.result.bspcoeff$n.group = 20
  
  simunum.bspcoeff.20 = rbind(simunum.bspcoeff.20,clunum.result.bspcoeff)
  seed = seed+10000*i
}

simunum.bspcoeff.20 = na.omit(simunum.bspcoeff.20)
write.csv(simunum.bspcoeff.20, file = "simunum_bspcoeff_20.csv", row.names = FALSE)

### Table 4: Kmeans on Coefficients part
## Summary analysis of the cluster number detection.
clunum.simunum.bspcoeff.20 = read.csv("simunum_bspcoeff_20.csv",header = TRUE)
clunum.simunum.bspcoeff.20.summary = clunum.simunum.bspcoeff.20%>%group_by(n.group, method,
                                                                     index, clu.num)%>%summarize(count = n())
clunum.simunum.bspcoeff.20.summary

Cluster Validation Simulation Study (Table 5)

• The Table 5 has been seperated in three part, and here has 1 of them: simuvid.raw.summary
• The simulation result for Raw data at Table 5 is at the end of this code file

##Clustering Validation Study Functions
# Hungarian Algorithm 
minWeightBipartiteMatching <- function(clusteringA, clusteringB) {
  require(clue)
  idsA <- unique(clusteringA)  # distinct cluster ids in a
  idsB <- unique(clusteringB)  # distinct cluster ids in b
  nA <- length(clusteringA)  # number of instances in a
  nB <- length(clusteringB)  # number of instances in b
  if (length(idsA) != length(idsB) || nA != nB) {
    stop("number of cluster or number of instances do not match")
  }
  
  nC <- length(idsA)
  tupel <- c(1:nA)
  
  # computing the distance matrix
  assignmentMatrix <- matrix(rep(-1, nC * nC), nrow = nC)
  for (i in 1:nC) {
    tupelClusterI <- tupel[clusteringA == i]
    solRowI <- sapply(1:nC, function(i, clusterIDsB, tupelA_I) {
      nA_I <- length(tupelA_I)  # number of elements in cluster I
      tupelB_I <- tupel[clusterIDsB == i]
      nB_I <- length(tupelB_I)
      nTupelIntersect <- length(intersect(tupelA_I, tupelB_I))
      return((nA_I - nTupelIntersect) + (nB_I - nTupelIntersect))
    }, clusteringB, tupelClusterI)
    assignmentMatrix[i, ] <- solRowI
  }
  
  # optimization
  result <- solve_LSAP(assignmentMatrix, maximum = FALSE)
  attr(result, "assignmentMatrix") <- assignmentMatrix
  return(result)
}


# Function to get cluster result
get.df.cluster = function(simu.all,n.group,seed){
  t = simu.all$t
  simu.all = simu.all[,-which(names(simu.all) %in% c("t"))]
  simu.all.mat = matrix(unlist(simu.all),ncol = 4*n.group)
  
  bks.1 = as.Date(quantile(unclass(as.Date(mindiff.date.1$date)), seq(0,1,length = 12)), origin = "1970-01-01")
  simu.basis = create.bspline.basis(rangeval = c(min(mindiff.date.1$date),max(mindiff.date.1$date)), breaks = bks.1, norder = 4) 
  simu.fd<-smooth.basis(argvals = t, y = simu.all.mat, simu.basis)$fd
  
  # fem on icl
  set.seed(seed)
  fem.icl <- funFEM(simu.fd,K = 4,model = "all",crit = "icl", init = "kmeans",eps = 1e-5) # 4 cluster solution
  df.fem.icl <- fem.icl$cls
  
  # fem on bic
  set.seed(seed)
  fem.bic <- funFEM(simu.fd,K = 4,model = "all",crit = "bic", init = "kmeans",eps = 1e-5) # 4 cluster solution
  df.fem.bic <- fem.bic$cls
  
  # kmeans on bsp coeff
  set.seed(seed)
  simu.fd.coef = t(simu.fd$coefs)
  coeff.k <- kmeans(simu.fd.coef, 4) # 4 cluster solution
  df.bsp.k <- coeff.k$cluster
  
  # Kmeans on smoothed pc scores
  range = c(as.numeric(min(t)),as.numeric(max(t)))
  bspFpcPen = fdPar(fdobj=simu.basis, Lfdobj=2, lambda = 2e6)
  ## We will explain this lambda selection in the next part
  smooth.fpc = pca.fd(simu.fd,nharm=3,harmfdPar=bspFpcPen)
  df.pcscore = smooth.fpc$scores
  set.seed(seed)
  fpc.k <- kmeans(df.pcscore, 4) # 4 cluster solution
  df.fpc.k <- fpc.k$cluster
  
  # Hungarian Alg
  real = rep(c(1,2,3,4),each = n.group)
  a = minWeightBipartiteMatching(df.bsp.k,real)
  df.bsp.k.1 = a[df.bsp.k]
  
  b = minWeightBipartiteMatching(df.fpc.k,real)
  df.fpc.k.1 = b[df.fpc.k]
  
  c = minWeightBipartiteMatching(df.fem.bic,real)
  df.fem.bic.1 = c[df.fem.bic]
  
  d = minWeightBipartiteMatching(df.fem.icl,real)
  df.fem.icl.1 = d[df.fem.icl]
  
  clu.result = data.frame(clu.real = real,
                          clu.bsp = df.bsp.k.1,
                          clu.fpc = df.fpc.k.1,
                          clu.fem.bic = df.fem.bic.1,
                          clu.fem.icl = df.fem.icl.1)
  return(clu.result)
}


# Accuracy test
get.clu.accuracy = function(df.clu, n.group){
  bsp.accu = sum(df.clu$clu.real == df.clu$clu.bsp)/(n.group*4) 
  fpc.accu = sum(df.clu$clu.real == df.clu$clu.fpc)/(n.group*4)
  fem.bic.accu = sum(df.clu$clu.real == df.clu$clu.fem.bic)/(n.group*4)
  fem.icl.accu = sum(df.clu$clu.real == df.clu$clu.fem.icl)/(n.group*4)
  return(c(bsp.accu,fpc.accu,fem.bic.accu,fem.icl.accu))
}


##Clustering Number Selection Validation Simulation
simuvid.real.20= data.frame(matrix(ncol = 4, nrow = 1))
colnames(simuvid.real.20) <- c("method","index","n.group","accuracy")
seed = 888
for (i in  1:200){
  set.seed(seed)
  df = generate.curve.real(20,seed = seed)
  cluvid.result = data.frame(matrix(ncol = 4, nrow = 4))
  colnames(cluvid.result) <- c("method","index","n.group","accuracy")
  cluvid.result$method = c("bsp","fpc","fem","fem")
  cluvid.result$index = c("all","all","bic","icl")
  cluvid.result$n.group = rep(20,each = 4)
  df.clu = get.df.cluster(df,n.group = 20,seed = seed)
  
  cluvid.result$accuracy = get.clu.accuracy(df.clu, 20)
  
  simuvid.real.20 = rbind(simuvid.real.20,cluvid.result)
  seed = seed+10000*i
}

## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(X) : infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'
## Error in svd(ginv(t(G) %*% G %*% W) %*% (t(G) %*% Ttilde %*% t(Ttilde) %*%  : 
##   infinite or missing values in 'x'

simuvid.real.20 = na.omit(simuvid.real.20)
write.csv(simuvid.real.20, file = "simuvid_real_20.csv", row.names = FALSE)

### Table 5: Summary the validation result
## This contains the Kmeans on Coeffs and FPC scores, and FEM BIC and ICL
simuvid.raw = read.csv("simuvid_real_20.csv",header = TRUE)
simuvid.raw.summary = simuvid.raw%>%
  group_by(n.group, method,index)%>%
  summarize(mean.accuracy = mean(accuracy),
            sd.accuracy = sd(accuracy),
            se.accuracy = sd(accuracy)/sqrt(200))
simuvid.raw.summary

2. Simulation on Raw Time Series Data

Simulation about Cluster Number Detection (Table 4 Raw Data Part)

## Kmeans on Raw Data 
## Select Number of Cluster 
simunum.realraw.20= data.frame(matrix(ncol = 4, nrow = 1))
colnames(simunum.realraw.20) <- c("method","index","clu.num","n.group")
seed = 888
for (i in 1:200){
  set.seed(seed)
  df = generate.curve.real(20,seed = seed)
  df = df[,-which(names(df) %in% c("t"))]
  clunum.result.raw = data.frame(matrix(ncol = 4, nrow = 1))
  colnames(clunum.result.raw) <- c("method","index","clu.num","n.group")
  clunum.result.raw$method = "kmeans on raw"
  clunum.result.raw$index = "average silhouette width"
  set.seed(seed)
  pamk.best <- pamk(df,krange=2:6)
  clunum.result.raw$clu.num = pamk.best$nc
  clunum.result.raw$n.group = 20
  
  simunum.realraw.20 = rbind(simunum.realraw.20,clunum.result.raw)
  seed = seed+10000*i
}

simunum.realraw.20 = na.omit(simunum.realraw.20)
write.csv(simunum.realraw.20, file = "simunum_realraw_20.csv", row.names = FALSE)

### Summary analysis of the cluster number detection.
clunum.sim.20.raw = read.csv("simunum_realraw_20.csv",header = TRUE)
clunum.sim.20.raw.summary = clunum.sim.20.raw%>%group_by(n.group, method,
                                                 index, clu.num)%>%summarize(count = n())
clunum.sim.20.raw.summary

Simulation about Cluster Validation (Table 5 Raw Data Part)

## Function for Cluster Result Validation 
get.clu.accuracy.raw = function(df.clu, n.group){
  # Hungarian Alg
  real = rep(c(1,2,3,4),each = n.group)
  a = minWeightBipartiteMatching(df.clu, real)
  df.clu.1 = a[df.clu]
  
  raw.accu = sum(real == df.clu.1)/(n.group*4) 
  return(raw.accu)
}

#### Start the Simulation
simuvid.realraw.20= data.frame(matrix(ncol = 4, nrow = 1))
colnames(simuvid.realraw.20) <- c("method","index","n.group","accuracy")
seed = 88
for (i in  1:200){
  set.seed(seed)
  df = generate.curve.real(20,seed = seed)
  df = df[,-which(names(df) %in% c("t"))]
  cluvid.raw.result = data.frame(matrix(ncol = 4, nrow = 1))
  colnames(cluvid.raw.result) <- c("method","index","n.group","accuracy")
  cluvid.raw.result$method = c("kmeans on raw")
  cluvid.raw.result$index = c("average silhouette width")
  cluvid.raw.result$n.group = 20
  set.seed(seed)
  df.clu <- kmeans(t(as.matrix(df)),4)
  cluvid.raw.clu = df.clu$cluster
  
  cluvid.raw.result$accuracy = get.clu.accuracy.raw(cluvid.raw.clu, 20)
  
  simuvid.realraw.20 = rbind(simuvid.realraw.20,cluvid.raw.result)
  seed = seed+10000*i
}
simuvid.realraw.20 = na.omit(simuvid.realraw.20)
write.csv(simuvid.realraw.20, file = "simuvid_realraw_20.csv", row.names = FALSE)

### Summary the validation result
simuvid.realraw = read.csv("simuvid_realraw_20.csv",header = TRUE)
simuvid.realraw.summary = simuvid.realraw%>%
  group_by(n.group, method,index)%>%
  summarize(mean.accuracy = mean(accuracy),
            sd.accuracy = sd(accuracy),
            se.accuracy = sd(accuracy)/sqrt(200))
simuvid.realraw.summary